MTS

So you were doing it QAYG (Quilt As You Go)?

I would suggest drawing a line on the batting straight down the middle - that way you have a guide to make sure your placement of each piece of the braid is always perfectly centered.

That would work especially well if you're using cornerstones up the middle.

I did this when I was making a Judith Larzelere-style quilt - it's also QAYG, but I needed those guidelines to keep the piecing (and quilt sandwich) from going all wonky on me.

Another source of the problem could be the type of batting you are using - some stretch more than others, and all that handling can have an effect.
I only use cotton for QAYG.